PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

50 RISKINESS LEVERAGE MODELSwant to give more attention to the extreme areas. In fact, a regulator’slist of properties for the riskiness leverage might includethat it1. be zero until capital is seriously impacted, and2. not decrease, because of the risk to the state guarantyfund.TVAR could be used as such a risk measure if the quantile ischosen to correspond to an appropriate fraction ® of surplus.This would be(x ¡ ®S)L Regulator (x)=1 ¡ F(®S) : (5.1)However, everyone recognizes that at some level of probabilitymanagement will have to bet the whole company. There isalways business risk.Management may more typically formulate its risk appetitein forms such as “For next year, we want not more than a 0.1%chance of losing all our capital, and not more than a 10% chanceof losing 20% of capital.” This is basically two separate VARrequirements, and can be satisfied by using the larger of the tworequired capital amounts. Or, as in the spreadsheet, managementmay choose to say something like, “We want our surplus to be1 1 2times the average bad result in the worst 2% of cases.”A (much too) simple example approximately satisfying (1) to(3) on management’s list consists of linear downside riskinessleverage:8< 0 for x¹ : (5.2)SThe value of ® is essentially the relative riskiness at the mean andat excess over mean equal to surplus. The value of ¯ is again anoverall scale factor. In the spreadsheet the allocations are nearlyindependent of the value of ®, and TVAR is used for the exam-